root(3)(25x^11)/root(3)(9w^2)
we need to rationalize the denominator first.
What we are looking for are factors that are multiples of the index, or perfect cubes.
root(3)(25x^11)/root(3)(9w^2)
9 * 3 = 27 meaning 3^3 is 27
w^2 *w = w^3 giving us another perfect cube rationalizing the denominator
root(3)(25x^11)/root(3)(9w^2)*root(3)(3w)/root(3)(3w) = (root(3)125 root(3)(w)root(3)(x^11))/(root(3)(27w^3)
In the numerator:
root(3)125 = 5 Is a perfect cube
root(3)w is fully simplified
root(3)x^9 * root(3)x^2 = root(3)x^11
x^(9/3) = x^3
root(3)27 root(3) w^3 This is the denominator
root(3)27 = 3
root(3)w^3 = w
put it all back together over a single fraction
(5x^3 root(3)(x^2)root(3)w)/(3w)